Different types of cory cats have different temperature requirements. Even though yours seemed to be doing fine at 82 and even 84 degrees, 80 is most likely too warm for their optimal health.
I suggest you check
http://www.planetcatfish.com to find the maximum temperature for your corys. If it's 78, your betta will be fine. As you've seen in this thread, some people have had success with bettas at lower temps, but I personally wouldn't go much lower for a betta.
The site is very comprehensive but difficult to navigate, especially if you start at the home page. Here's another starting point that might help you:
http://www.planetcatfish.com/core/search.php
You'll need to find out the scientific names of your cories if you don't know them already.
Good luck. I hope they are one of the more heat-tolerant varieties -- 78 or 78.8 might be the upper range.